There are several way the "league" allows any given team to win.
1. Be a league (NFL only) founding team with original ownership still in tact. Steelers, Giants, Bears all qualify. This is the golden ticket.
2. Build a new stadium. Indebting a city toward the future of the "league" will grant you a winner for a given amount of time. Most of this will occur prior to voting on the stadium proposal. Must have fans drunk on success as the grossly misuse public funds. (49ers, Colts, Cardinals)
3. Ownership must have ties to a major league sponsor. (Seahawks, Broncos)
4. Don't be an aging city in a decrepit stadium, where the fanbase is already built in. The "league" built itself on these people, and knows they will always be there. It does not need to bend games for these folks. They drink the cool-aid each year, and are the backbone of our league, but require no special treatment. Not even #2 can help this scenario. Browns, Lions, and our beloved Bills are notable members here.
All other winners are a revolving pool chosen at random. It's rumored that there is a meeting where that years winners are chosen. It's also rumored that at this meeting Virginia McCaskey sacrifices a lamb here, and herself, the Rooney's, Mara's, and Goodel all drink the blood. These are purely rumors and can't be substantiated.